-16t^2+60t+6=0

Solution for -16t^2+60t+6=0 equation:

Simplifying
-16t2 + 60t + 6 = 0

Reorder the terms:
6 + 60t + -16t2 = 0

Solving
6 + 60t + -16t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 30t + -8t2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + 30t + -8t2)' equal to zero and attempt to solve:

Simplifying
3 + 30t + -8t2 = 0

Solving
3 + 30t + -8t2 = 0

Begin completing the square.  Divide all terms by
-8 the coefficient of the squared term: 

Divide each side by '-8'.
-0.375 + -3.75t + t2 = 0

Move the constant term to the right:

Add '0.375' to each side of the equation.
-0.375 + -3.75t + 0.375 + t2 = 0 + 0.375

Reorder the terms:
-0.375 + 0.375 + -3.75t + t2 = 0 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + -3.75t + t2 = 0 + 0.375
-3.75t + t2 = 0 + 0.375

Combine like terms: 0 + 0.375 = 0.375
-3.75t + t2 = 0.375

The t term is -3.75t.  Take half its coefficient (-1.875).
Square it (3.515625) and add it to both sides.

Add '3.515625' to each side of the equation.
-3.75t + 3.515625 + t2 = 0.375 + 3.515625

Reorder the terms:
3.515625 + -3.75t + t2 = 0.375 + 3.515625

Combine like terms: 0.375 + 3.515625 = 3.890625
3.515625 + -3.75t + t2 = 3.890625

Factor a perfect square on the left side:
(t + -1.875)(t + -1.875) = 3.890625

Calculate the square root of the right side: 1.97246673

Break this problem into two subproblems by setting 
(t + -1.875) equal to 1.97246673 and -1.97246673.

Subproblem 1
t + -1.875 = 1.97246673

Simplifying
t + -1.875 = 1.97246673

Reorder the terms:
-1.875 + t = 1.97246673

Solving
-1.875 + t = 1.97246673

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '1.875' to each side of the equation.
-1.875 + 1.875 + t = 1.97246673 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + t = 1.97246673 + 1.875
t = 1.97246673 + 1.875

Combine like terms: 1.97246673 + 1.875 = 3.84746673
t = 3.84746673

Simplifying
t = 3.84746673

Subproblem 2
t + -1.875 = -1.97246673

Simplifying
t + -1.875 = -1.97246673

Reorder the terms:
-1.875 + t = -1.97246673

Solving
-1.875 + t = -1.97246673

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '1.875' to each side of the equation.
-1.875 + 1.875 + t = -1.97246673 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + t = -1.97246673 + 1.875
t = -1.97246673 + 1.875

Combine like terms: -1.97246673 + 1.875 = -0.09746673
t = -0.09746673

Simplifying
t = -0.09746673

Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {3.84746673, -0.09746673}
Solution
t = {3.84746673, -0.09746673}